Police are investigating whether "criminal activity" took place following allegations of inappropriate behaviour towards women by the senior Liberal Democrat peer Lord Rennard.

Scotland Yard disclosed that it had been approached by party officials in the wake of claims Lord Rennard had exploited his former position as chief executive to proposition women and to touch them inappropriately.

"The Metropolitan Police Special Investigations Command has been approached by officials in the Liberal Democrat Party and is working with them to ascertain whether or not criminal activity has taken place," a spokesman said.

The party said last night it would "engage fully" with the police on the issue.

"We can confirm that the party has had an invitation to attend a 'stakeholder meeting' at Scotland Yard to discuss the involvement of the police in any investigation into Chris Rennard," a Lib Dem spokesman said.

"The party will fully engage with the police on this issue and continue to encourage anyone with allegations of a criminal nature to contact the police."

Lord Rennard, who was the Lib Dem's key election strategist and adviser to a succession of party leaders, has strongly denied the allegations made against him by a series of Lib Dem women.

A ComRes poll for The Independent showed support for the party slumping to just 8% - the lowest level recorded by ComRes - one point behind Ukip on 9%.

Meanwhile, party leader Nick Clegg has come under sustained pressure to explain what exactly he had known about the claims and what he had done about them.

The Lib Dems initially insisted that Mr Clegg had known nothing about them until a Channel 4 News report broke the story on Thursday.

On Sunday, however, the Deputy Prime Minister returned from holiday in Spain to concede that his office had heard "indirect and non-specific concerns" as far back as 2008.

He said that his then chief of staff Danny Alexander had put the concerns to Lord Rennard who denied any inappropriate behaviour. The following year the peer stepped down as chief executive citing ill health.

But yesterday The Daily Telegraph published a 2010 email exchange with Mr Clegg's chief of staff Jonny Oates, in which it gave details of the dates and locations of four alleged incidents between 2003 and 2007 involving Lord Rennard, and made clear it knew the identities of the women who had complained.

It asked whether Mr Clegg was aware of the claims and whether it was true that Mr Alexander and Lib Dem MP Jo Swinson had looked into them.

Mr Oates responded at the time: "It is untrue to state that Mr Clegg was made aware of the incidents you allege. Given this fact, it is obviously untrue to state that Mr Clegg asked Jo Swinson or anyone else to carry out an investigation into the incidents that you allege."

Mr Clegg's position was not helped when Lib Dem president Tim Farron, referring to the way the case had been handled, said the party had "screwed this up".

Speaking to BBC Radio Solent days ahead of Thursday's crunch Eastleigh by-election, Mr Clegg said: "I totally understand people have got lots and lots of questions but I hope I have given a full, frank, honest account.

"I have got nothing to hide, the party has nothing to hide. We have now got to listen to the women who feel they weren't properly listened to and get to the truth and that is what we will do."